Acampus survey of owls indicates that 7% are charming, 4% are modest, and 3% are both charming and modest. find the probability that an owl is modest, given that he/she is charming. given that a student isn't modest, what is the probability that they are not charming?

P(modest | charming) = 0.4286

P(not charming | not modest) = 0.896

Step-by-step explanation:

This is a conditional probability problem.

Let A and B be two dependent events, then:

The probability of A given B is written as:

P (A | B) =

So:

The probability that an OWL is modest given that he/she is charming is:

P (modest | charming) =

P (modest | charming) =

P (modest | charming) = 0.4286

Then, the probability that a student is not modest is:

The probability that a student is not charming and not modest is:

So:

P(not charming | not modest) =

P(not charming | not modest) =

P(not charming | not modest) = 0.9583

Basically divide each fraction to get the simplified version of each answer. You divide each fraction by the highest multiple.
4/16 can be divided by 4 to get 1/4
12/18 can be divided by 6 to get 2/3
4/10 can be divided by 2 to get 2/5
16/20 can be divided by 4 to get 4/5